How can I align a new object to the camera view with Python?
Since you want to align the object with the current view (and not the camera), you need to extract that view through the view 3D's region_3d (rv3d in the example below), then assign its rotation to the object you want to align the view with:

import bpy
def view3d_find( return_area = False ):
    # returns first 3d view, normally we get from context
    for area in bpy.context.window.screen.areas:
        if area.type == 'VIEW_3D':
            v3d = area.spaces[0]
            rv3d = v3d.region_3d
            for region in area.regions:
                if region.type == 'WINDOW':
                    if return_area: return region, rv3d, v3d, area
                    return region, rv3d, v3d
    return None, None

r3d, rv3d, v3d = view3d_find()

# Add new plane which will become the context object
bpy.ops.mesh.primitive_plane_add()

bpy.context.object.rotation_euler = rv3d.view_rotation.to_euler()